Time-reversal (sometimes referred to as phase-conjugation) has characteristics that make it highly attractive for radar applications. These include automatic tracking of moving targets and self-focusing, regardless of atmospheric turbulence without a need for any prior knowledge or iterative adaptive processing. However, the time-reversal proposed to date is limited to one-way distortion compensation. The operation of the conventional single-pass time-reversal radar is shown in FIG. 1 and is as follows:
TABLE 1Operational principle of conventional single-pass time-reversal.BEAMBEAM CHARACTERISTICSa′A pilot beam illuminates the area that includes an intendedtarget.b′Part of the beam is reflected from the target. Its wavefront isdistorted by the shape of the target.bBeam propagates through the atmosphere. Wavefront isfurther distorted.cPart of beam b arriving at transmitter/receiver (Tx/Rx) is time-reversed by Time-Reversal Mirror (TRM), and is reflectedback toward the target. The wavefront c partially resembles b.c′After transmission through the atmosphere, the beam c′resembles b′ and so is focused on the target. Coherent beamfocusing on a target
As a result, the returned beam is coherently summed and focused at the target (c′). However, one should note that the coherent beam focusing is limited to the target side only, not at the transmitter/receiver (Tx/Rx) side, as can be appreciated by the distorted wavefront (b, c). This feature of target side-only focusing of the conventional time-reversal has limited its use for imaging or radar applications, which require compensation of distortion occurred by round trip and beam focusing at both target and Tx/Rx.
In order to obtain an image using time-reversal, the DORT (Decomposition of the time reversal operator) method has been proposed by Prada et al. (Prada C, Manneville S, Spoliansky D and Fink M, “Decomposition of the time reversal operator: detection and selective focusing on two scatterers,” J. Acoust. Soc. Am. 99 2067-76, 1996.).
The method reconstructs targets by back propagation of the first temporal eigenvectors obtained by singular value decomposition. However, it has limited application to narrowband signal with a small number of discrete target points. Also, it requires information on detailed background boundary condition in order to back propagate the wave and to reconstruct an image. Further, these operations require a significant amount of computation time.